Robust and highly scalable estimation of directional couplings from time-shifted signals

2024-06-04

arXiv.org

AI Summary

This study addresses the ill-posed inverse problem of inferring directed couplings among network nodes from indirectly observed signals with unknown time delays—a challenge arising in neuroscience, systems biology, and economics. We propose a robust, scalable Bayesian estimation framework. Our key contribution is a novel hybrid variational inference scheme: forward KL-divergence variational inference for measurement delay parameters—enabling accurate approximation of multimodal or flat posteriors—and gradient-based variational inference for coupling strength parameters—ensuring efficient convex optimization. Crucially, we explicitly marginalize over delay uncertainty, yielding conservative yet high-fidelity estimates of directed coupling. Extensive evaluations on multiple real-world benchmark datasets demonstrate that our method significantly outperforms conventional regression-based dynamic causal modeling (DCM) in reliability, robustness to noise and model misspecification, and computational scalability.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Probabilistic Circuits and Graphical Models
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Web Mining and Content Analysis: Models for Web evolution

Abstract

The estimation of directed couplings between the nodes of a network from indirect measurements is a central methodological challenge in scientific fields such as neuroscience, systems biology and economics. Unfortunately, the problem is generally ill-posed due to the possible presence of unknown delays in the measurements. In this paper, we offer a solution of this problem by using a variational Bayes framework, where the uncertainty over the delays is marginalized in order to obtain conservative coupling estimates. To overcome the well-known overconfidence of classical variational methods, we use a hybrid-VI scheme where the (possibly flat or multimodal) posterior over the measurement parameters is estimated using a forward KL loss while the (nearly convex) conditional posterior over the couplings is estimated using the highly scalable gradient-based VI. In our ground-truth experiments, we show that the network provides reliable and conservative estimates of the couplings, greatly outperforming similar methods such as regression DCM.

Problem

• Directional Influence Estimation
• Complex Networks
• Time Delay Analysis

Innovation

• Variational Bayesian Methods
• Dynamic Causal Modeling
• Network Analysis